Select the correct answerA can complete a work in 12 days, B in 15 days. Find the time taken by them: If A leaves two days before the scheduled completion of the work.Options9 4/79 1/69 5/69 2/3

To solve this problem, we first need to find the rate at which A and B can complete the work.

1. A can complete the work in 12 days, so A's work rate is 1/12 of the work per day.
2. B can complete the work in 15 days, so B's work rate is 1/15 of the work per day.

When A and B work together, their combined work rate is the sum of their individual rates. So, A and B together can do (1/12 + 1/15) of the work per day.

To simplify this, we find a common denominator, which is 60. So, A's work rate is 5/60 and B's work rate is 4/60. Therefore, their combined work rate is (5/60 + 4/60) = 9/60 = 3/20 of the work per day.

Now, we know that A leaves 2 days before the work is completed. This means that for the last 2 days, only B is working. So, in those 2 days, B can do 2 * (1/15) = 2/15 of the work.

Subtracting this from the total work (which is 1), we find that A and B together must do (1 - 2/15) = 13/15 of the work.

To find out how long this takes, we divide the amount of work (13/15) by their combined work rate (3/20). This gives us (13/15) / (3/20) = 52/9 days.

So, the total time taken by them is the time they work together (52/9 days) plus the 2 days that B works alone, which is (52/9 + 2) = 70/9 = 7 7/9 days.

Therefore, the correct answer is not in the options provided. The correct answer should be 7 7/9 days.